Having yet to see anything official from Sprint, a leaked screen capture suggests that the carrier will begin rolling out the Galaxy S III Jelly Bean update as of today, October 25. Assuming this proves to be accurate, this would mean Sprint is the first U.S. based carrier to do so. That aside though, the update looks to be arriving as L710VPALJ7, Android 4.1 Jelly Bean. The one catch, while the update is expected to begin rolling out today, the leaked screen capture notes that the update will be pushed to all customers over a few week period. Simply put, while the roll-out should begin today — you may not actually see it for a few weeks time. Regardless, we suspect that all Galaxy S III users with Sprint will want it now and that being the case — grab your handset and navigate to Menu -> Settings -> About device to try and get the process started. Otherwise, sit back and wait for the update notification to arrive on your handset.